I usually turn off my GPS to save batery. However, I would like to be able to turn the GPS on remotely and get its coordinates (e.g. by e-mail). Today a friend of mine almost lost her phone on the forest... In case next time it were my phone, I would like to be able to locate it easily.
I tried Android Device Manager as mentioned here but it gives me the coordinates of the last time I had my GPS on and it does NOT turn the GPS on to give me the latest/current coordinates.
I happened to have a Samsung phone, so you can use the FindMyMobile service, which can get you the coordinates of your phone even if your GPS was off when you lost it. However, you need to register in the web beforehand and authorize the Remote Controls in the menu Settings/Lock Screen and Security/Find My Mobile/[Log in with your Samsung details] and then activate Remote Controls.
It would be good to know any alternative for those not having a Samsung though...
This does not answer the main question, but addresses the side conversation in comments about why battery life should not be a significant concern to leaving location enabled for lost phone situations.
If you use well-written applications, having location services enabled will not mean that they will drain your battery. These features should only drain your battery if you are actively using them.
You can see which applications are using location services under Settings->Security and Location->Location (exact menu varies by version). This screenshot is from Android 8, but I think this feature is present at least from Android 6.
